A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

作者：Nie Yu^*

来源：Transportation Research Part B: Methodological , 2011, 45(2): 329-342.

DOI：10.1016/j.trb.2010.07.001

• System optimum dynamic traffic assignment
• Cell transmission model
• The Merchant-Nemhauser (M-N) model
• Marginal cost analysis
• Flow holding back

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop's second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.

• 出版日期2011-2
• 单位西北大学